550 Scientific Proceedings, Royal Dublin Society. 
both kinds lying at points of intersection of tetragonal, trigonal, and 
digonal axes, and also of the planes of symmetry. The two kinds 
are present in the same numerical proportions. The generic 
symmetry is holohedral, being that of class 28 in Sohncke’s list. 
A case of tetrahedral hemihedrism of the cubic system. 
Tf the radii of two sets of spheres are very nearly in the pro- 
portion requisite for the assemblage in which the larger spheres. 
have the closest-packed arrangement of figs. 1 and 2 and the 
smaller just fit into the larger interstices between them,’ but the 
smaller are just too large to allow of the larger spheres being in 
contact, a different arrangement gives closest-packing of the 
spheres. This arrangement is obtained if the larger spheres, 
which will be not quite in contact when arranged as in the closest- 
packed arrangement referred to, approach one another uniformly 
in groups of four, till the four mutually touch, while = 
the different kinds of spheres continue in contact. 
The assemblage formed in this way may be regarded 
as consisting of groups each composed of eight spheres, 
four of each kind tetrahedrally arranged (fig.10). In 
it each large sphere is in contact with six small ones, 
and also with three large ones, making nine contacts, and each 
small sphere has six contacts as in the previous case.” The type of 
Fig. 10. 
1 See p. 547. 
2 The centres of the spheres in a closest-packed homogeneous structure of this kind! 
do not precisely give a possible equilibrium arrangement for mutually -repellent particles. 
of two kinds, because the equality of the distances between the centres of the spheres: 
of different radius which touch one another would then involve equality of the repul— 
sions subsistizg between the two different kinds of particles placed at these centres, 
and this equality does not necessarily exist in the modified arrangement referred to. 
For each force which acts on a particle is not now, as in the previous case, balanced 
by a similar opposite force, and, for the forces which act on a particle to be in statical 
equilibrium, they must bear certain ratios to one another which depend on their 
mutual inclinations. And in the case before us these inclinations are such that the: 
pressures between nearest different particles, and therefore their distances apart, will 
have to form two different sets which are not alike, but slightly different one from the 
other. A slight modification of the arrangement of the sphere-centres is therefore 
necessary to obtain the actual equilibrium arrangement possible for two kinds of 
particles in the case under consideration, but this modification will be one which: 
ig quite symmetrical (compare p. 529). 
ee. ee ed 
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elt 
